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Paper   IPM / M / 12870
School of Mathematics
  Title:   Nonplanarity of unit graphs and classification of the toroidal ones
1.  H. R. Maimani
2.  M. R. Pournaki
3.  S. Yassemi (Joint with A. K. Das)
  Status:   Published
  Journal: Pacific J. Math.
  Vol.:  268
  Year:  2014
  Pages:   371-387
  Supported by:  IPM
The unit graph of a ring R with nonzero identity is the graph in which the vertex set is R, and two distinct vertices x and y are adjacent if and only if x+y is a unit in R. In this paper, we derive several necessary conditions for the nonplanarity of the unit graphs of finite commutative rings with nonzero identity, and determine, up to isomorphism, all finite commutative rings with nonzero identity whose unit graphs are toroidal.

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